Download Recognition of Operating States of a Medium

The 13th Scandinavian International Conference on Fluid Power, SICFP2013, June 3-5, 2013, Linköping, Sweden
Recognition of Operating States of a Medium-Sized Mobile Machine
T. Krogerus, M. Hyvönen, K. Raivio* and K. Huhtala
Department of Intelligent Hydraulics and Automation, Tampere University of Technology, Tampere, Finland
E-mail: [email protected], [email protected], [email protected]
*Department of Information and Computer Science, Aalto University School of Science, Espoo, Finland
Abstract
In this study the main goal was to study the operating states of a medium-sized mobile machine.
The measured time series data were analysed to find frequent episodes (sequences of operating
states) to which the conditional probabilities were then calculated. The time series data were
first segmented to find events. One or more segments build up an event which can be
interpreted to be an operating state. The segments were then clustered and classified. The
segment class labels were interpreted as events. As a result, a list of rules was established. The
rules describe causal connections between consecutive operating states and transition
probabilities from 1st state to 2nd state. The recognized operating states were further analysed to
be used in diagnosis of the operation of the machine and focusing the diagnostics on certain
operating states.
Keywords: Mobile machine, analysis, diagnostics, operating state, hydraulics, time series,
segmentation, episode, event, piecewise linear regression, clustering, classification, association
rules, quantization error
the measured time series data of a mobile machine requires
segmentation of the time series data to find the events. Time
series segmentation is often used as a pre-processing step in
time series analysis applications. An episode is again
defined as a collection of events that occur relatively close
to each other in a given partial order [6]. Causal connections
are then searched for by analysing the consecutive episodes.
1 Introduction
Technological development has produced mobile machines
that are remotely operated [1] directly or work
autonomously [2] while only being supervised remotely.
These machines demand increased monitoring and analysis
[3] of the performance and operating states of these
machines when there is no person present inside the
machine. If the operating states of the machine can be
recognized during work tasks, causal connections between
consecutive operating states can be determined and
furthermore, diagnostics can be focused on specific
operating states.
The operation of the machine can be further analysed using
the recognized operating states. Diagnostics can be focused
on certain operating states. Usually these are the ones that
have the biggest changes in the analysed variables. Most
information in regard to the detection of anomalies is
obtained from these operating states.
Typically, in a modern mobile machine there is already a lot
of information available about the operation of the machine,
e.g. process and control data through communication buses,
which can be used in analysis. In addition to this, condition
monitoring specific sensors can also be added to the system.
When all this information from communication busses and
additional sensors are recorded, it leads to the generation of
a huge amount of data. High dimensionality complicates the
processing of time series data especially from the pattern
recognition point of view [4]. A time series is defined as a
collection of observations made sequentially in time [5].
2 Description of the studied mobile machine
The studied mobile machine, called IHA-machine [7], was
engineered at the Department of Intelligent Hydraulics and
Automation at Tampere University of Technology. It was
designed to serve as a platform where different types of
research could be conducted concurrently. The research
platform is shown in fig. 1.
An overview of the hydraulic systems of IHA-machine,
which are related to the analysis performed in this study, is
given here. More details are presented in [7]. Figure 2 shows
a simplified hydraulic circuit of the closed loop hydrostatic
transmission (HST) of IHA-machine. It also shows the
added sensors and most important auxiliary components that
provide safety and maintenance functions.
In order to analyse the time series data of mobile machines,
detectors of events to find frequent episodes need to be first
created, and after that some higher level description, for
example probability distributions or quantization error
method [3] should be used. Finding frequent episodes from
379
Both the diesel engine and the pump are connected to the
main PLC (Programmable Logic Controller) of the machine
via the CAN bus. They also have separate control units,
which are connected to the CAN bus, offering data from
integrated sensors. Therefore, via the CAN bus several
parameters related to the operation of these components, e.g.
diesel load and HST pump angle, can be monitored and
recorded for later analysis.
Every wheel of the machine is equipped with a slow speed
hydraulic hub motor, with a displacement of 470 cm3/r.
Each motor has a pressure controlled holding brake and an
integrated sensor for measuring rotational speed. A separate
hydraulic gear pump provides the power needed by the
steering system. The steering of the machine can be
controlled using proportional flow control valve and two
symmetrically placed hydraulic cylinders. The work
hydraulics of the IHA-machine are based on digital
hydraulics [7,8], but this part of the machine is not studied
here.
Figure 1: Studied mobile machine [7].
The main source of power is a 100 kW four-cylinder diesel
engine. The HST pump has a displacement of 100 cm3/r and
contains various integrated hydraulic components, sensors
and electronics to implement the closed-loop control of the
swivel angle and the data communication.
Figure 2: Hydrostatic transmission of studied mobile machine [7].
and noise reduction and possibly down sampling using
moving average filtering for each measurement.
3 Events and causal connections from time
series
In the method used in this study to find causal connections
from the time series data, the data have been segmented to
extract operating states. One or more segments build up an
event which can be interpreted to be an operating state. A
state is defined as a combination of the patterns of the
selected variables. The sequences of operating states can
then be further analysed to discover association rules from
the sub-sequences. The method depicted in fig. 3 will be
explained in more detail in the following sections.
Figure 3: Events and causal connections from time series.
3.1 Pre-processing
3.2 Segmentation
The data have to be scaled before segmentation. This
guarantees that all variables have an equal effect on the
segmentation result. Representative statistics of the data are
needed in order to be able to scale the measurements. To do
that, all the variables of the data should have enough
variation. The data range and distribution used to compute
the statistics should correspond to those of the whole data
set. Pre-processing also includes the elimination of outliers
In segmentation, the time series data are transformed into
piecewise linear representation. A segment is a contiguous
subset of a time series. In this study, the time series data is
segmented using the sliding window method with piecewise
linear regression [5]. In this method, curves are
approximated with lines: see fig. 4.
380
undesirable. Of course, the above post-processing methods
will change single state distributions and transition
probabilities.
New samples are added to the segment until cumulative
squared estimation error exceeds a predefined threshold.
Another possible criterion is the maximum of squared error
in the segment. Several measurements can be segmented
together. Thus, they have common cost function and the cost
is computed by summing all the measurements. The
measurements define together the edges of segments.
The sequence of segment classes will be interpreted as a
sequence of states. Each state has a discrete label and a time
stamp. Sequences from multiple sources can be combined
into one sequence. Possible sources for sequences are the
segmentation results of two separate measurement groups.
Different methods or features can be used in each
segmentation.
The sliding window segmentation method is well suited to
online segmentation, because only the preceding samples
are needed to define the edges. However, the method can be
quite slow if the sampling rate is high. There are several
modifications of the sliding window segmentation algorithm
and there are other more efficient segmentation methods, but
unfortunately most of them are not very suitable for online
analysis. This is because the methods expect that the whole
sequence is available at the time of segmentation.
3.5 Search for frequent episodes
Frequent episodes can be searched from the sequences using
the Apriori algorithm [6,11]. The algorithm finds the most
probable sub-sequences from a sequence starting from the
sub-sequence of length one. The length of the sequence is
increased by one every round. The effectiveness of method
is based on the principle that only those episodes which
have had all their sub-episodes frequent enough in the
previous round are possible candidates for frequent
episodes.
3.3 Classification of segments
Pre-processed segments are then clustered and classified.
Clustering is the process of organizing objects into groups
whose members are similar in some way. A cluster is
therefore a collection of objects which are similar between
them and are dissimilar to the objects belonging to other
clusters. Clustering can be performed using hierarchical
methods or k-means algorithm [9].
The algorithm has two possibilities for initial search of
length of two episodes. It is possible to search for serial or
parallel episodes from the sequence. In the case of serial
episodes, the order in which the states have occurred on the
time scale is important, but in the case of parallel episodes
the primary interest is to find out if the states occurred in the
same time window or not. When longer episodes are
searched for, it is, of course, possible to search for more
complicated combinations of parallel and serial episodes if
desired.
The parameters of piecewise linear regression lines are used
as features. One choice is to use the slopes of lines as
features. Also, the offset and the length of segment can be
used as additional features. The number of segment clusters
has to be defined, or a validation index should be used to
select a suitable amount of clusters [10]. It is not necessary
to cluster all the available segments, as some of them can be
classified using cluster prototype vectors defined using a
representative set of segments. Each cluster is presented by
a d-dimensional prototype vector (also known as: weight,
codebook, model, reference)
= [m , … , m ], where d is
equal to the dimension of the input vectors. It is useful to
save these prototype vectors, to classify another set of
segments or to analyse classes or classification results later.
The algorithm has several parameters, which have to be
defined. These are the minimum frequency for an episode to
be considered as interesting, the length of window used in
the search, maximum length of episode and minimum
confidence. The last one is actually a threshold for the
conditional probability of a sequence.
The sequence occurrence rates are converted to probabilities
by dividing the rate by the number of all search windows.
The sequence probabilities P(A, B) are further converted to
conditional probabilities P(B|A) using single state
probabilities: see eq. 1.
3.4 Post-processing segmentation results
Segment classes can be analysed using their prototype
vectors. In case slope coefficients are used as segment
features, prototypes can easily be visualized to find
interpretation for classes or states: see fig. 5.
P(B|A) =
When the classified segments are converted to events, it is
possible to remove non-interesting segments or events.
Events describe the behaviour and actions of the system. For
example, a segment class with around zero slope
coefficients for all measurements can be considered
unusable. Events built from these segments can be removed
before further analysis, because later analysis will be
focused on those operating states where changes in the
analysed variables are at their biggest which means that the
slopes of the feature vectors are steep. It is also possible to
combine subsequent segments with the same class labels if a
lower number of detected states are wanted or a high
probability of transitions from states to themselves is
P(A, B)
P(A)
(1)
Here, state A precedes state B, and P(A) is the probability of
state A. The target is to find causal connections between
states which occur frequently enough compared to other
sequences in which either one of the two states occur.
4 Measured data for analysis
Different test cases were defined and 79 different test drives
were carried out to obtain measurement data from different
operating states, which were then analysed. These test cases
consist of a combination of different work tasks: driving
straight, turning, going uphill, downhill, over obstacles,
emergency braking, reversing, different driving speeds, and
381
these test drives on gravel. Table 2 shows the measured
variables during these test drives which were then used in
the analysis. Measured time series data were analysed using
two different data sets, namely variables of machine driving
behaviour (velocity/turnings) and hydrostatic transmission.
slow and fast rise time of driving speed. Two different
ground types were used: asphalt and gravel. The machine
was driven with either a test person on-board, or remotely
using a laptop computer. An added load of 1000 kg was also
used in some of the test drives. Some combinations of task
scenarios were driven several times. Table 1 shows cases of
Table 1: Cases of test drives on gravel.
Case id Description
Speed Control
Load Special definitions
6-1
Uphill
40 %
Person
X
6-2
Downhill
20 %
Person
X
6-3
Uphill-stop-uphill start
40 %
Person
X
6-4
Uphill
40 %
Person
-
6-5
Downhill
20 %
Person
-
6-6
Uphill-stop-uphill start
40 %
Person
-
7-1
Turn right - over obstacle
20 %
Computer -
Obstacle: block of wood (right tyre)
7-2
Turn right - over obstacle
40 %
Computer -
Obstacle: block of wood (right tyre)
7-3
Turn right - over obstacle
20 %
Computer -
Obstacle: block of wood (left tyre)
7-4
Turn right - over obstacle
40 %
Computer -
Obstacle: block of wood (left tyre)
8-1
Driving straight
40 %
Computer X
Slow: rise time 1.5 s to max. speed
8-2
Driving straight
40 %
Computer X
Fast: rise time 0.5 s to max speed
8-3
Driving straight
40 %
Person
X
Slow: rise time 1.5 s to max. speed
8-4
Driving straight
40 %
Person
X
Fast: rise time 0.5 s to max speed
8-5
Driving straight
40 %
Computer -
Slow: rise time 1.5 s to max. speed
8-6
Driving straight
40 %
Computer -
Fast: rise time 0.5 s to max speed
8-7
Driving straight
40 %
Person
-
Slow: rise time 1.5 s to max. speed
8-8
Driving straight
40 %
Person
-
Fast: rise time 0.5 s to max speed
9-1
Driving straight
40 %
Person
-
Emergency braking
10-1
Straight-right-straight-left-straight 20 %
Person
-
10-2
Straight-right-straight-left-straight 40 %
Person
-
10-3
Straight-right-straight-left-straight 20 %
Person
X
10-4
Straight-right-straight-left-straight 40 %
Person
X
10-5
Straight-right-straight-left-straight 20 %
Computer X
10-6
Straight-right-straight-left-straight 40 %
Computer X
10-7
Straight-right-straight-left-straight 20 %
Computer -
10-8
Straight-right-straight-left-straight 40 %
Computer -
11-1
Directly reversing
40 %
Computer -
Slow: rise time 1.5 s to max. speed
11-2
Directly reversing
40 %
Computer -
Fast: rise time 0.5 s to max speed
12-1
Simulation of normal operation
Person
382
-
Hydrostatic transmission
Driving behaviour
Table 2: Measured variables during test drives.
Signal
Range
Unit
Steering reference
-16384…16383 -
Frame angle
193,1…117,1
°
Rotational speed of front left tyre
-∞...∞
r/s
Rotational speed of front right tyre -∞...∞
r/s
Rotational speed of rear left tyre
-∞...∞
r/s
Rotational speed of rear right tyre
-∞...∞
r/s
Diesel rotational speed reference
0…2200
rpm
HST pump angle reference
-1000…1000
‰
Diesel rotational speed
0…2200
rpm
Diesel load
0…100
%
HST pump measured angle
-1000…1000
‰
Pressure at port A
0…500
bar
Pressure at port B
0…500
bar
.
Next, the pre-processed measurements were segmented
using sliding window segmentation with piecewise linear
regression. Cumulative squared error function with the
threshold 0.3 was used to define the edges of segments. Data
from all the test drives were segmented similarly using two
groups of measurements. An example of segmentation of
one test drive in the case of driving behaviour related
measurements (frame angle and rotational speed of front
left) is shown in fig. 4.
5 Recognition of operating states from
measurement data
Measurements were scaled to zero mean and unit variance
before the analysis. For this, measurement statistics from
eleven representative test drives were collected. Moving
average filtering was also used to get rid of situations when
segment is intercepted by noise in measured variables.
Frame angle
4
2
0
-2
-4
00:00
00:10
00:20
00:30
00:40
00:50
00:40
00:50
Rotational speed of front left tyre
4
2
0
-2
00:00
00:10
00:20
00:30
Figure 4: Time series segmentation of case 12-1. Frame angle and rotational speed of front left tyre are shown as examples.
The measurements are normalized to zero mean and unit variance for segmentation and the length of time series is 50 s.
383
The segments of eleven representative test drives were
clustered using k-means clustering with Davies-Bouldin
validation index [10] and segment slopes as features. In tab.
3 is defined the basic steps of k-means algorithm.
clusters and the one giving minimum validation index value
was selected. In this study, the optimal number of clusters
for driving behaviour variables was found to be 27, and for
hydrostatic transmission variables 29.
Table 3: Steps of K-means clustering.
As a result of clustering, the segments of representative test
drives were clustered and a prototype vector for each cluster
was computed. These models were used to classify the
segments of other test drives. Prototype vectors of clusters
for driving behaviour measurements are shown in fig. 5. The
lines in the subplots describe the behaviour of the signal in a
particular state. The signal is constant or increases or
decreases at a certain rate. A state is a combination of the
patterns of the selected variables. For example, in state 27
(the far right column) the values of the 1st and 6th variable
increase and the others decrease.
K-means clustering
1. Initialize: select a set of K candidate cluster centres
2. Assign each data point to the closest cluster centre
3. Set the cluster centres to the mean value of the points in
each cluster
4. Repeat Steps 2 and 3 for a fixed number of iterations or
until there is no change in cluster assignments
‖
J=
The grouping in k-means algorithm is done by minimizing
the sum of squares of distances between data and the
corresponding cluster centres according eq. 2, where K is
the number of groups and N is the number of sample/feature
vectors,
is sample/feature vector and
is the mean of
the data points in set i, i.e. prototype of cluster i and it is
calculated according eq. 3.
=
1
N
−
‖
(2)
(3)
The segmentation results were further processed by
combining consecutive segments belonging to the same
class. The segment class labels generate an event sequence.
For each event a time stamp is computed by averaging
sample time stamps of the segment.
Clustering was repeated five times for every number of
clusters and the result with minimum quantization error was
selected. The number of clusters was varied from 10 to 30
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
Figure 5: Prototype segments for 1st variable set. The rows correspond to variables and columns to operating states.
which are unique over both measurement sets. As a result,
hydrostatic transmission related events are labelled between
28 and 56. In fig. 6 classified segments with the event labels
of one test drive are shown.
Two event sequences were built for each test drive. Event
labels generated using hydrostatic transmission related
measurements are shifted by the number of segment classes
for driving behaviour measurements to obtain event labels
384
200
Frame angle
150
100
00:00:00
1
00:00:30
00:01:00
Rotational speed of front left tyre
00:01:30
00:00:30
00:01:00
Rotational speed of front right tyre
00:01:30
00:00:30
00:01:00
Rotational speed of rear left tyre
00:01:30
00:00:30
00:01:00
Rotational speed of rear right tyre
00:01:30
00:00:30
00:01:00
00:01:30
00:01:00
00:01:30
0
-1
00:00:00
1
0
-1
00:00:00
1
0
-1
00:00:00
1
0
-1
00:00:004
x 10
1
Steering reference
0
-1
00:00:00
1 8 13 3 2 18 2111
00:00:30
17
22
17
14 22 2 1916 17
8
22
17
14 4 26 2711 7 2512 22 17
Figure 6: Time series (case 12-1) of length 1min 45s are plotted using different colours for each event. The labels of events are
shown on the bottom row.
According to the first rule in the table, state 45 occurs nine
times and there is an over 88% probability that state 15 will
follow.
The probabilities of the events which occur in the test drives
are shown in fig. 7. Some of the segment classes are more
probable than others. Usually, the slopes of segments in
such classes or states are near zero. Thus, the classes
correspond to constant movement or operation without any
changes.
0.12
For each test drive two sequences corresponding to the
measurement sets were combined. The new sequence has
events with labels from 1 to 56.
0.1
0.08
Frequent serial episodes of length 2 were searched for from
these sequences. The time stamps were converted to discrete
values, because the original algorithm is designed to process
these.
0.06
0.04
Serial episodes with a certain probability were found. The
probabilities were further converted to conditional
probabilities using eq. 1 to find out how probable it is that
one state occurs when a certain state has already occurred.
In tab. 4 serial episodes with the highest conditional
probability are shown. The probability of an episode in the
studied sequences is also shown, as well as the overall
probability of the first events of episodes.
0.02
0
0
10
20
30
40
50
60
Figure 7: Probabilities of all events over all cases. There
are total 56 different events: 27 for 1st variable sets and 29
for 2nd variable sets.
385
Here, the neuron whose weight vector is closest to the input
sample vector is called the BMU, denoted by c.
Table 4: Serial episodes and the event probabilities used to
compute episode conditional probabilities. There are in
total 758 events. Episodes with first event occurring three
times or less are left out as well as episodes with conditional
probability of less than 0.3.
45 → 15
P(A, B)
0.01055
P(A)
0.01187
n(A)
9
0.8889
46 → 15
0.00660
0.00792
6
0.8333
31 → 22
0.02243
0.02902
22
0.7727
44 → 15
0.02111
0.02770
21
0.7619
53 → 22
0.00792
0.01055
8
0.7500
43 → 22
0.00396
0.00528
4
0.7500
55 → 22
0.00660
0.00923
7
0.7143
30 → 22
0.01583
0.02243
17
0.7059
51 → 15
0.02243
0.03562
27
0.6296
20 → 10
0.00660
0.01055
8
0.6250
48 → 17
0.01715
0.02902
22
0.5909
41 → 22
0.02111
0.03694
28
0.5714
5 → 33
0.00528
0.00923
7
0.5714
6 → 20
0.00396
0.00792
6
0.5000
6 → 33
0.00396
0.00792
6
0.5000
34 → 37
0.01187
0.02375
18
0.5000
22 → 39
0.04881
0.10422
79
0.4684
37 → 31
0.01055
0.02507
19
0.4211
24 → 33
0.00528
0.01319
10
0.4000
39 → 17
0.02375
0.06069
46
0.3913
10 → 41
0.00396
0.01055
8
0.3750
17 → 33
0.03430
0.09631
73
0.3562
35 → 17
0.01451
0.04222
32
0.3438
25 → 32
0.00264
0.00792
6
0.3333
35 → 32
0.01319
0.04222
32
0.3125
15 → 48
0.02507
0.08047
61
0.3115
‖ = min{‖ −
‖}
(4)
After this, a certain threshold can be set which determines
the greatest distance on which recognition occurs. So when
the method is tested the distances between the sample
vectors from the testing data and all the cluster prototype
vectors are calculated. If the minimum distance is bigger
than the threshold value set beforehand, then this sample
vector is treated as an anomaly, which can be either a new
operating or a fault state.
P(B|A)
After anomalies have been detected and proved to be faulty
operating states, data from these states can be used to detect
and identify them in the future. However, in this study there
were no data available from faulty states.
Figure 8 shows the quantization error of all the classified
segments of the 1st data set. There are altogether 302
segments. In turn, fig. 9 shows the quantization error of the
2nd data set. There are altogether 377 segments. Based on
these quantization errors, thresholds can be set to separate
possible anomalies from normal states. In these figures few
larger quantization errors can be seen, which complicates
the detection of anomalies. In this case, some of the
anomalies could be mixed with normal states. This could
perhaps still be improved by selecting a different number of
clusters or even another clustering method. Only the kmeans clustering method was used in this study. But also
longer and more versatile test drives than those which are
used here would improve the situation and reduce the
number of spikes in the quantization error.
Figure 10 shows the quantization error of state number 22,
which is the most probable state in the test drives: see fig. 7.
84 segments were classified as state 22. Here, only a few of
the quantization error values are significantly larger than the
rest of the values. Thus, in case of state number 22 the
definition of the threshold to detect anomalies is more
straightforward.
Distance from closest prototype vector
A→B
e =‖ −
6 Analysis of operation using recognized states
After recognition of the operating states, these can be further
analysed to study the operation of the machine. On the basis
of earlier research results [3] it was noticed that the biggest
effects of different fault states were at the transient stages of
the hydraulic system in which the changes in the pressure
and volume flows were at their highest. Therefore analysis
will be focused on operating states where the slopes of the
feature vectors are steep and when changes in the analysed
variables are at their biggest.
1st variable set
2
1.5
1
0.5
0
0
100
200
Number of classified segments
300
Figure 8: Quantization error of all classified segments of 1st
data set.
The quantization error method [3,12,13] was used to study
the operation of the machine, and it is based on the distance
calculation, Euclidian distance, which is shown in eq. 4.
386
Distance from closest prototype vector
to study the operation of the machine using the quantization
error method. It is noted that this is an on-going work.
2nd variable set
7
The data-driven methods described in this study can be
implemented to different kinds of mobile machines.
Insufficient sensor information may limit the number of
applications, but the analysis methods in general are not
restricted to a specific machine type. The thresholds in
segmentation and anomaly detection need be defined based
on specific applications and need specific knowledge about
the operation of the system. The selection of critical
measurement signals describing the operation of the
machine also requires knowledge about the machine.
6
5
4
3
2
1
0
0
Nomenclature
100
200
300
Number of classified segments
Designation
Distance from closest prototype vector
Figure 9: Quantization error of all classified segments of 2nd
data set.
A
B
c
e
J
K
State number 22
1.5
1
N
n(A)
P(A)
P(A, B)
P(B|A)
0.5
0
20
40
60
Number of classified segments
80
Denotation
st
1 state
2nd state
Best-matching unit (BMU)
Quantization error
Sum of squares clustering function
Number of groups/clusters
Prototype vector
Prototype vector chosen as BMU
Number of sample vectors
Number of state A
Probability of state A
Sequence probability
Conditional probability
Data/feature vector
Unit
[-]
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[-]
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[-]
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[-]
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References
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Figure 10: Quantization error of state number 22.
7 Conclusions
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